Tentukan hasil integral berikut! (x^2-1) √2x^3-6x+7 dx

integral

∫(x² -1) √(2x³ -6x +7) dx

u =2x³ - 6x +7
du/dx = 6x² - 6
du = 6(x²-1) dx
x²-1 dx = 1/6 du

∫(x² -1) (2x³ - 6x + 7) dx =
= ∫ 1/6 (u)¹/² du
= (1/6)(2/3) U³/² + c
= 1/9 U √ U + c
= 1/9 (2x³ - 6x +7) √(2x³ -6x + 7) + c